A cereal company includes a prize in 55% of its cereal boxes. If the company produced 27,000 packages of cereal last week, how many packages contained a prize ?

a. 4,909 b. 12,150

c. 13,500 d. 14,850

4.4 warm-up

9

5.4 Inverse, 5.4 Inverse, Contrapositive, and Contrapositive, and Indirect ReasoningIndirect Reasoning

You will review different forms You will review different forms of reasoning.of reasoning.

Before we begin, there are Before we begin, there are some terms you need to some terms you need to

remember.remember.

Conditional: If A, then B.

Inverse:If not A, then not B.

Converse: If B, then A.

PardekooperPardekooper

p q

q p

~p ~q

Contrapositive:

If not B, then not A.

~q ~p

PardekooperPardekooper

Conditional StatementsConditional StatementsIf-then Statement:

one statement depends on the result of a condition.

Example:Example:

''If Deanna eats the last cookie, then Leon will buy more.'‘

hypothesishypothesis conclusionconclusion

hypothesis conclusion

1st part,If ____

2nd part,then ____

If , then

You forgotp q

PardekooperPardekooper

Converse StatementsConverse Statements

switch the hypothesis and the conclusion

Example:Example:

''If Leon buys some more cookies, then Deanna will eat the last one.'‘

conclusionconclusion hypothesishypothesis

conclusion hypothesis

1st part,If ____

2nd part,then ____

If , then

You forgotq pagain

PardekooperPardekooper

Negation StatementsNegation Statements

the denial of a statement

If a statement is true,

then its negation is

false.

If a statementis false,then its

negation istrue.

IfIf this hadthis had not not been an actual emergencybeen an actual emergency, then, then the attention signal you just heard wouldthe attention signal you just heard would not not

have been followed by official information, news, have been followed by official information, news, or instruction.or instruction.

MeadowsMeadows

&&

PardekooperPardekooper

Negation StatementsNegation StatementsExample: .

this had not been an actual emergency

the attention signal you just heard would not have been followed by official information, news, or instruction

hypothesis: conclusion:

Note: The inverse of p → q is ~p → ~q. ‘~’ means ‘not.’

the attention signal you just heard would not have been followed by official information, news, or instruction

this had not been an actual emergencyconclusion:

hypothesis:

IfIf the attention signal you just heard wouldthe attention signal you just heard would notnot have been followed have been followed by official information, news, or instructionby official information, news, or instruction, then, then this hadthis had not not been been an actual emergencyan actual emergency..

Note: The contrapositive of p → q is ~ q → ~ p.

Contrapositive Contrapositive StatementsStatements

created by negating the hypothesis and conclusion of the converse of the given

conditional.

Here comes the Here comes the assignmentassignment

AssignmentWorkbook

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